Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

Non-singular space-times with a negative cosmological constant: V. Boson stars

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.     

A convenient synthesis and the mesomorphic properties of new chiral ferroelectric thiobenzoates

A secondary chiral (R)-(?)-2-alcohol underwent the Mitsunobu reaction with triphenylphosphine, diethyl azodicarboxylate and ethyl 4-hydroxybiphenylcarboxylate, resulting in the desired (S)-(+)-product with high enantiomeric purity (>99% ee), with the chiral branched chain attached to the biphenyl. This method is operationally simple and provides the very important chiral precursor in good yields (62% in dry THF and 72% in dry Et₂O). The condensation of the (S)-(+)-acid chloride from this material and a suitable 4-n-alkylthiophenol in toluene in the presence of pyridine or triethylamine furnishes the chiral (S)-(+)-thiobenzoate liquid crystals in good yields (80–83% in pyridine and 65–68% in Et₃N). (S)-(+)-4-(1-Methylheptyloxy)biphenyl 4-alkylthiobenzoates are abbreviated (S)-MHOBSn , where n varies from 4 to 10 and denotes the number of carbon atoms in the alkyl chain. DSC, polarizing microscopy and X-ray diffraction showed that the (S)-MHOBSn series possesses a rich phase polymorphism: two highly ordered tilted phases CrG* and SmI*, as well as the ferroelectric smectic C (SmC*) and chiral nematic (N*) phase. In this series, the seldom observed transition between the chiral phases SmI*–SmC* is seen. All the compounds possess stable enantiotropic SmC* and N* phases. The existence of weak intermolecular hydrogen-bonding in (S)-MHOBSn was confirmed by FTIR spectroscopy.     

KIDs are Non-Generic

We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that nonexistence of global symmetries implies, generically, non-existence of local ones. As part of the argument, we prove that generic metrics do not possess any local or global conformal Killing vectors.submitted 22/02/04, accepted 28/07/04     

Singular Yamabe Metrics and Initial Data with Exactly Kottler–Schwarzschild–de Sitter Ends

We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler–Schwarzschild–de Sitter metrics in regions of infinite extent. From the purely Riemannian geometric point of view, this produces complete, constant positive scalar curvature metrics with exact Delaunay ends which are not globally Delaunay. The ends can be used to construct new compact initial data sets via gluing constructions. The construction provided applies to more general situations where the asymptotic geometry may have non-spherical cross-sections consisting of Einstein metrics with positive scalar curvature. Submitted: October 19, 2007. Accepted: February 11, 2008.     

Non-Singular,Vacuum, Stationary Space-Times with a Negative Cosmological Constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant. Submitted: December 12, 2005. Accepted: May 22, 2006.     

On the invariant mass conjecture in general relativity

An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, PolandSupported in part by the Polish Ministry of Science Research Project CPBP 01.2 and by the NSF Grant PHY8503072 to Yale University     

Study of the Phase Situation in 4-n-pentylphenyl-4′-n-heptyloxythiobenzoate (7S5)

Results of measurements of the specific heat of 4-n-pentylphenyl-4′-n-heptyloxythiobenzoate in the temperature range from about 90 K to about 370 K are presented. They were carried out with an adiabatic calorimeter, a differential scanning calorimeter and a polarizing microscope. Adiabatic calorimetry revealed four anomalies in the specific heat vs. temperature curve viz., two associated with transitions in the solid phase, one with melting and one with the liquid-crystalline nematic-to-isotropic phase transition. Also, two modifications of the solid, stable and metastable, were found to exist. In addition, the DSC method applied in the 285 K to 370 K range revealed a smectic C phase, but only when the sample is being cooled. The polarizing microscope showed the structural polymorphism of the solid phase in the 297 K to 327 K range to be more complex than would stem from adiabatic calorimetry and DSC measurements alone. It also confirmed the occurence of the S_c phase on cooling as ascertained by the DSC method.     

Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass

We extend the validity of Brill’s axi-symmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.